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# Solutions for Chapter 14: Probability Rules!

## Full solutions for Stats Modeling the World | 4th Edition

ISBN: 9780321854018

Solutions for Chapter 14: Probability Rules!

Solutions for Chapter 14
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##### ISBN: 9780321854018

This textbook survival guide was created for the textbook: Stats Modeling the World, edition: 4. Chapter 14: Probability Rules! includes 56 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 56 problems in chapter 14: Probability Rules! have been answered, more than 58166 students have viewed full step-by-step solutions from this chapter. Stats Modeling the World was written by and is associated to the ISBN: 9780321854018.

Key Statistics Terms and definitions covered in this textbook
• a-error (or a-risk)

In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error).

• Acceptance region

In hypothesis testing, a region in the sample space of the test statistic such that if the test statistic falls within it, the null hypothesis cannot be rejected. This terminology is used because rejection of H0 is always a strong conclusion and acceptance of H0 is generally a weak conclusion

• Average run length, or ARL

The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.

• Biased estimator

Unbiased estimator.

• Box plot (or box and whisker plot)

A graphical display of data in which the box contains the middle 50% of the data (the interquartile range) with the median dividing it, and the whiskers extend to the smallest and largest values (or some deined lower and upper limits).

• Center line

A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.

• Coeficient of determination

See R 2 .

• Conidence level

Another term for the conidence coeficient.

• Continuous distribution

A probability distribution for a continuous random variable.

• Correction factor

A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .

• Covariance

A measure of association between two random variables obtained as the expected value of the product of the two random variables around their means; that is, Cov(X Y, ) [( )( )] =? ? E X Y ? ? X Y .

• Dependent variable

The response variable in regression or a designed experiment.

• Event

A subset of a sample space.

• F distribution.

The distribution of the random variable deined as the ratio of two independent chi-square random variables, each divided by its number of degrees of freedom.

• F-test

Any test of signiicance involving the F distribution. The most common F-tests are (1) testing hypotheses about the variances or standard deviations of two independent normal distributions, (2) testing hypotheses about treatment means or variance components in the analysis of variance, and (3) testing signiicance of regression or tests on subsets of parameters in a regression model.

• Fisherâ€™s least signiicant difference (LSD) method

A series of pair-wise hypothesis tests of treatment means in an experiment to determine which means differ.

• Gamma random variable

A random variable that generalizes an Erlang random variable to noninteger values of the parameter r

• Generating function

A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function

• Geometric random variable

A discrete random variable that is the number of Bernoulli trials until a success occurs.

• Goodness of fit

In general, the agreement of a set of observed values and a set of theoretical values that depend on some hypothesis. The term is often used in itting a theoretical distribution to a set of observations.